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YAVUZ, EMEL

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EMEL

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2006 - 20072
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Author: Şen, A.Has files: true

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    On Janowski starlike functions
    (Springer International Publishing Ag, Gewerbestrasse 11, Cham, Ch-6330, Switzerland, 2007) Çağlar, Mert; Şen, A.; Owa, Shigeyoshi; YAVUZ, EMEL; POLATOĞLU, YAŞAR; 108339; 199370; 111202
    For analytic functions f(z) in the open unit disc U with f(0) = 0 and f'(0) = 1, applying the fractional calculus for f(z), a new fractional operator D-lambda f(z) is introduced. Further, a new subclass F-lambda(*)(A, B) consisting of f(z) associated with Janowski function is defined. The objective of the present paper is to discuss some interesting properties of the class F-lambda(*)(A, B). Copyright (c) 2007.
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    A study on the generalization of Janowski functions in the unit disc
    (2006-01) Bolcal, Metin; Şen, A.; YAVUZ, EMEL; POLATOĞLU, YAŞAR; 199370; 111202
    Let › be the class of functions w(z), w(0) = 0, |w(z)| < 1 regular in the unit disc D = {z : |z| < 1}. For arbitrarily fixed numbers A 2 (¡1,1), B 2 (¡1,A), 0 • fi < 1 let P(A,B,fi) be the class of regular functions p(z) in D such that p(0) = 1, and which is p(z) 2 P(A,B,fi) if and only if p(z) = 1+((1¡fi)A+fiB)w(z) 1+Bw(z) for some function w(z) 2 › and every z 2 D. In the present paper we apply the principle of subordination ((1), (3), (4), (5)) to give new proofs for some classical results concerning the class S⁄(A,B,fi) of functions f(z) with f(0) = 0, f0(0) = 1, which are regular in D satisfying the condition: f(z) 2 S⁄(A,B,fi) if and only if z f 0 (z) f(z) = p(z) for some p(z) 2 P(A,B,fi) and for all z in D.